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fatigue: overstressing and understressing

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While teaching some students from old textbooks, I found reference to "understressing and overstressing" as producing effects into fatigue limits. Looking at classical papers like W SCHUTZ, A HISTORY OF FATIGUE Engineering Fracture Mechanics Vol. 54, No. 2, pp. 263-300, 1996, he says that the theory of understressing was largely a mistake due to statistically poor testing. However, I see some chinese papers still talk of understressing, see below.

On the other hand, I know for sure overload of cracks does produce crack retardation and even arrest, so some companies I think use overloads to induce compressive residual stresses at the notches and make safe life possible with higher stress amplitudes. Do you know papers about this? Do you have experience? Usually overloads are discussed with random fatigue crack propagation, which does not include the case of crack arrest and safe life design. But I guess it should not be too difficult to estimate when DK becomes lower than DK_Th.

A lot of unnecessary confusion was caused by the "under-" and "overstressing" effects maintained by Kommers and others [166-168] -- from 1930 until long after WW II. Had they existed, they would have been of no practical significance. However, a statistical [169, 170] check of the "coaxing" due to understressing proved they were nonexistent. Kommers had overlooked the relatively large scatter of the fatigue limit; that is, the alleged effects had occurred by accidentally using specimens with a high fatigue limit for the understressing tests. The following example, however, shows the influence of Kommers' claims: in a German paper of that time, in all seriousness the importance of cautiously breaking-in the crankshaft of a new automobile engine is stressed in order that its fatigue limit be thus increased by "understressing"!

Using scanning electron microscopy, transmission electron microscopy, and X-ray diffraction, some microscopic experiments and analyses were performed to explain the microscopic mechanism of strengthening under low-amplitude loads below the fatigue limit (SLAL). The experimental results show that the microscopic mechanism of SLAL could be dislocation-accumulation and grain boundary strengthening to low-strength material without strengthening by surface heat treatment. After SLAL, the microstructure imperfections can be improved and the fatigue resistance can be enhanced. Macroscopically, the fatigue strength and life of structures can be obviously improved and increased.

Since you are writing a book on shakedown and numerical methods, I would love to talk with you more about residual stresses (RS) and fatigue for example.I would love that your book answered some big doubts I have, rather than explaining the numerical methods only. The SD community seems to me to be hiding on a ivory tower and I am not sure which problems they solve. For civil engineers? For mech eng? For geotechnical one? So if I were you, I would make a big effort to connect SD theory with existing engineering practices.

We know for sure that RS are beneficial (if compressive) for fatigue life ---- this I suspect was originally proved by shoot peening which was invented in Germany and the United States in the late 1920s and early 1930s. I was first wondering how long do they last? Do they relax in, say, 1000 cycles?But then you find even in Wikipedia that “A study done through the SAE Fatigue Design and Evaluation Committee showed what shot peening can do for welds compared to welds that didn't have this operation done. The study claimed that the regular welds would fail after 250,000 cycles when welds that had been shot peened would fail after 2.5 million cycles, and that failure would occur outside of the weld area. This is part of the reason that shot peening is a popular operation with aerospace parts. However, the beneficial prestresses can anneal out at higher temperatures.”

I wonder however if this is material specific.

So more questions:

1) in shakedown theory, we are told that RS (to some extent) do not change the limit loads...so why they change fatigue loads?

2) Dang Van has the merit to have introduced concepts of SD into fatigue, but the original criterion only really worked with elastic stresses like any other multiaxial criterion. Only later the French at Ecole Polytechnique are introducing more ingredients into his “mesoscopic” theory to predict SD at mesoscopic level. Things however become incredibly complicated.

3) in some codes, like Eurocodes to design steel structures, we are told to neglect RS and design as they were zero – is this to be conservative?

4) while teaching some students from old textbooks, I found reference to "understressing and overstressing" as producing effects into fatigue limits.Looking at classical papers likeW SCHUTZ, A HISTORY OF FATIGUE Engineering Fracture Mechanics Vol. 54, No. 2, pp. 263-300, 1996, he says that the theory of understressing was largely a mistake due to statistically poor testing.From the point of view of plasticity theory, understressing if anything should perhaps enhance annealing, so it is strange that it would have a positive effect.

5) I know for sure overload of cracks does produce crack retardation and even arrest, although I know also that even manual of the Nasa crack growth best code, NASGRO, suggests not to take into account this too much, unless you are "expert", and be better conservative.

6) In smooth specimen, there is bound to be confusion about response to understressing or overstressing because possible variations in the manner different materials or even different specimens will behave. It is a question of how internal discontinuities, inclusions, and surface scratches, residual stress from processing, etc., reacted to the overstress or understress.

7) in notches, assuming overstress or understress caused local inelastic response at the notch root, the response will uniformly be the same in all metallic materials – Overload will induce increased fatigue limit. Underload will diminish it. This is obvious from simple Neuber conversion that will indicate compressive local residual stress after an overload and tensile residual stress after understress. The consequent change in local stress ratio at the notch root will cause obvious effect on fatigue response.

8) Finally, in long cracks (and not in small ones), an overstress will retard the crack. At worst, an understress will at most momentarily accelerate the crack, the effect being negligible because of quick recovery in closure.

9) Some people argue about this “coaxing” or understressing, rather from a material point of view, as strain-induced precipitation-hardening.

10) I spoke to various people and they all agree that Kommers coaxing effect was due to incorrect fatigue testing, before we had any fatigue test standards and much was done with rotating beam tests. But also that companies like RR, PW, PWC, GE, BMW, Snecma, Boeing, Lockheed etc. do not believe in so called retardation effects in crack propagation. Companies do not allow a life extension between inspection (a life credit) based on retardation in FCP for a DTA or any similar analysis.

11) Whilst retardation does produce changes in FCP behavior for some materials it also should be noted that in some Ti alloys and other more complex crystal structures that it produces acceleration after overloads. The USAF and some others have spent much money and time on studying overloads but still are in a quandary as to whether to allow for life credits for them.

12) the Australians have a theory of “naturally occuring cracks” in operational aircrafts, which is not the same concept used for Damage Tolerance, where you artificially introduce a large defect, both to be conservative in calculation and experiments, and also to avoid the terrible complication of studying short crack effects. The Australians say there is little if any retardation associated with an overload in “naturally occurring cracks”. No one really believes that the high loads actually produce retardation.

13) For cold working (and I guess shot peening), we have a completely different level of plasticity hugely greater than that seen due to an overload in a flight spectra. The same thing applies for cold proof tests. The extent of the plasticity in the F111 proof test was so great that it causes cracking on nominally compressive members. The high loads in a flight spectrum just do not have this effect, which is what Schutz may have said, although he was probably not in this context. It is the old story that is emphasised in the fatigue test Standard ASTM E647-13a where it is stated that results obtained using the ASTM test methodoloy as outlined in the main body of the standard are not transferable to operational (real life) structures. This is conventional wisdom (otherwise it would not be in the test standard, and would not be in Shutz's paper.)

14) So although I seem to have heard companies use overloads to induce compressive residual stresses at the notches and make safe life possible with higher stress amplitudes, I am not sure.